This is complex. It seems logical to deduce that all the customers in other EC countries are EC VAT registered (hence the EC Sales Lists for goods transported from the UK); and that the Dutch warehouse is not a Customs/Freezone Warehouse (hence the charge for Duty).
On this assumption, I would expect the VAT Place of Supply to be Holland for all sales of goods transported from Holland to customers registered for VAT in other EC countries.
Ordinarily, one would then expect the vendor to register for Dutch VAT, to reclaim the Dutch Import VAT and to zero-rate their sales to the customers registered for VAT in other EC countries.
But there are an almost bewildering number of possibilities here.
The transport agent could also act as the import agent, maybe also as Dutch Fiscal Representative in selling on the goods fom Holland. The Dutch agent should be recording the Dispatch on its own EC Sales List. But if this is what is happening, this would be a poor choice for the vendor, as Dutch Import VAT cannot be reclaimed by the vendor (it might be paid and recharged by the transporter to the vendor).
Alternatively, the transporter/import agent might exercise an "Onward Supply Relief". This is a mechanism whereby the importer is not required to pay Import VAT if a VAT registered customer is already identified in another country and the goods are transported to them promptly. Again, the Dutch agent should record the Dispatch on its own EC Sales List. But overall this is a better solution, provided the vendor is not required to register for Dutch VAT, as they do not miss out on reclaimed Dutch Import VAT. But is this really what is happening? Is the transport agent really acting as import agent and recording the onward sale as a Dutch Dispatch on behalf of the vendor?
It is even possible that the Dutch VAT authorities might simply waive the need for the vendor to register for VAT, since all its sales will be zero-rated. But even if thi is permitted, if the sales invoices are issued by the vendor showing a UK VAT registration number, but the goods are imported into Holland via a Dutch VAT registration number, I can only assume that a "deemed" Acquisition from Holland takes place in the UK; plus an onward sale to the other EC country; which would presumably qualify as a deemed triangulation. There is some legal support for this, but it is far from clear.
The simplest solution, to make sure this all works correctly, is for the vendor to register for Dutch VAT and to record the Dutch Dispatch on their own Dutch EC Sales List, making the sales under their own Dutch VAT registration number; and making the Dutch Import under their own Dutch VAT registration number (and either reclaiming the Dutch Import VAT on their own Dutch VAT return, or using the "Onward Supply Relief" if they qualify). The question would then become: is it worth the cost of registering and maintaining a Dutch VAT registration, if another option is possible (e.g. one of the above)? In which case, it seems that professional advice would be best in this instance, as the complexities reach even beyond what the VAT laws envisaged.
Hope it helps?